If Ω is a ball in Rn (n ≥ 2), then the boundary integral operator of the double layer potential for the Laplacian is self-adjoint on L2(∂Ω). In this paper we prove that the ball is the only bounded Lipschitz domain on which the integral operator is self-adjoint.

The idea of the present paper is to discuss certain integral properties of Aleph function and multivariable’s general class of polynomials. We establish certain new double integral relations pertaining to a product to a multivariable’s general class of polynomials and Aleph function.

Symmetry can play an important role in the study of boundary value problems, which are a type problem mathematics that involves finding solutions to differential equations subject given conditions. Integral transforms crucial solving ordinary (ODEs), partial (PDEs), and integral equations. This article focuses on extending single-valued Sawi transform double-valued ST, we call double (DS) trans...

The double integral sliding mode synchronization method is studied for a class of super chaotic systems. Both the unknown parameters and uncertain nonlinear functions are considered for the driven and response chaotic systems. It is worthy pointing out that a kind of input nonlinearity is taken into consideration when the synchronization controller is designed. The uncertainties are very comple...

A family of continuous biorthogonal functions related to an elliptic analog of the Gauss hypergeometric function is constructed. The key tools used for that are the elliptic beta integral and the integral Bailey chain introduced earlier by the author. The relationship with the Sklyanin algebra and elliptic analogs of the Faddeev modular double are discussed in detail. §

This paper is concerned with the problem of scattering of time-harmonic electromagnetic waves from penetrable diffraction gratings in the 2D polarization case. We propose a new, weakly singular, integral equation formulation for the scattering problem which is proved to be uniquely solvable. A main feature of the new integral equation formulation is that it avoids the computation of the normal ...

Geometric sensitivity for single photon emission computerized tomography (SPECT) is given by a double integral over the detection plane. It would be useful to be able to explicitly evaluate this quantity. This paper shows that the inner integral can be evaluated in the situation where there is no gamma ray penetration of the material surrounding the pinhole aperature. This is done by converting...

This text introduces 1) New Regularized Combined Field Integral Equations (CFIE-R) for the solution of frequency-domain sound-hard scattering problems, and, 2) Fast, high-order algorithms for the numerical solution of the CFIE-R and related integral equations. Like the classical Combined Field Integral Equation (CFIE), the CFIE-R are unikely-solvable integral equations based on use of single an...

An accelerated boundary integral method for Stokes flow of a suspension of deformable particles is presented for an arbitrary domain and implemented for the important case of a planar slit geometry. The computational complexity of the algorithm scales as O(N) or O(N logN), where N is proportional to the product of number of particles and the number of elements employed to discretize the particl...

A seminal technique of theoretical physics calledWick’s theorem interprets the Gaussian matrix integral of the products of the trace of powers of Hermitian matrices as the number of labelled maps with a given degree sequence, sorted by their Euler characteristics. This leads to the map enumeration results analogous to those obtained by combinatorial methods. In this paper we show that the enume...